Abstract—This paper presents a novel design of an anisogrid

composite aircraft fuselage by a global metamodel-based

optimization approach. A 101-point design of numerical

experiments (DOE) has been developed to generate a set of

individual fuselage barrel designs and these designs have further

been analyzed by the finite element (FE) method. Using these

training data, global metamodels of all structural responses of

interest have been built as explicit expressions of the design

variables using a Genetic Programming approach. Finally, the

parametric optimization of the fuselage barrel by genetic

algorithm (GA) has been performed to obtain the best design

configuration in terms of weight savings subject to stability,

global stiffness and strain requirements.

Index Terms—Composite fuselage structure, anisogrid design,

genetic programming, metamodel.

I. INTRODUCTION

In order to keep air transport competitive and safe, aircraft

designers are forced for minimum weight and cost designs.

Carbon composite materials combined with lattice structures

for the next generation fuselage design have the potential to

fulfill these requirements. This novel design of a lattice

composite fuselage has been investigated recently for a new

weight-efficient composite fuselage section [1].

Based on the conceptual fuselage design obtained by

topology optimization with respect to weight and structural

performance [2], [3], the parametric optimization of the

composite lattice fuselage to obtain the optimal solution

describing the lattice element geometry is performed in this

paper. This detailed design process is a multi-parameter

optimisation problem, for which a metamodel-based

optimization technique is used to obtain the optimal lattice

element geometry. Since one of the design variables, the

number of helical ribs, is integer in the optimization of a

lattice composite fuselage structure, a discrete form of genetic

algorithm (GA) [4], [5] is used to search for the optimal

solution in terms of weight savings subject to stability, global

stiffness and strain requirements. Finally, the skin is

interpreted as a practical composite laminate which complies

with the aircraft industry lay-up rules and manufacturing

requirements.

Manuscript received February 14, 2015; revised July 27, 2015. This work

was supported in part by the European Commission and the Russian

government within the EU FP7 Advanced Lattice Structures for Composite

Airframes (ALaSCA) research project.

D. Liu is with the Faculty of Science, University of East Anglia, Norwich,

NR4 7TJ, UK (e-mail: dianzi.liu@uea.ac.uk).

Xue Zhou is with the Faculty of Business, Environment and Society,

Coventry University, Coventry, CV1 5FB, UK.

V. V. Toropov is with the School of Engineering and Materials Science,

Queen Mary University of London, London, E1 4NS, UK.

II. DESIGN OF EXPERIMENTS

The quality of the metamodel strongly depends on an

appropriate choice of the Design of Experiments (DOE) type

and sampling size. A uniform Latin hypercube DOE based on

the use of the Audze-Eglais optimality criterion [6], is

proposed. The main principles in this approach are as follows:

The number of levels of factors (same for each factor) is

equal to the number of experiments and for each level

there is only one experiment;

The points corresponding to the experiments are

distributed as uniformly as possible in the domain of

factors. There is a physical analogy of the Audze-Eglais

optimality criterion with the minimum of potential energy

of repulsive forces for a set of points of unit mass, if the

magnitude of these repulsive forces is inversely

proportional to the squared distance between the points:

21 1

1min

P P

p q p pq

UL

(1)

where P is the number of points, Lpq is the distance between

the points p and q (p≠q) in the system. Minimizing U

produces a system (DOE) where points are distributed as

uniformly as possible, see Fig. 1.

Fig. 1. Designs of experiments (100 points) generated by the conventional

(left) and optimal (right) Latin hypercube technique [7].

III. GENETIC PROGRAMMING (GP)

The genetic programming code was first developed

according to the guidelines provided by Koza [8], then further

implemented by Armani [9]. The common genetic operations

used in genetic programming are reproduction, mutation and

crossover, which are performed on mathematical expressions

stripped of their corresponding numerical values. Since GP

methodology is a systematic way of selecting a structure of

high quality global approximations, selection of individual

regression components in a model results in solving a

combinatorial optimization problem. In our case of design

optimization, the program represents an empirical model to be

used for approximation of a response function. A tree

structure-based typical program, representing the

Metamodels for Composite Lattice Fuselage Design

Dianzi Liu, Xue Zhou, and Vassili Toropov

International Journal of Materials, Mechanics and Manufacturing, Vol. 4, No. 3, August 2016

DOI: 10.7763/IJMMM.2016.V4.250 175

expression 2321 / xxx , is shown in Fig. 2.

These randomly generated programs are general and

hierarchical, varying in size and shape. GP's main goal is to

solve a problem by searching highly fit computer programs in

the space of all possible programs that solve the problem. This

aspect is the key to find near global solutions by keeping

many solutions potentially close to minima (local or global).

The evolution of the programs is performed through the

action of the genetic operators and the evaluation of the

fitness function.

IV. FINITE ELEMENT SIMULATIONS AND MARGINS OF

SAFETY

Two FE models used in the analysis were based on a

relatively coarse mesh and a much finer mesh that

corresponds to a converged solution found from a mesh

sensitivity study. The coarse mesh FE simulations, that are an

order of magnitude faster, still reveal the most prominent

features of the structural response and hence have been used

in the analysis of 101 designs corresponding to the DOE

points. Then, the obtained optimal solution was validated by

the analysis with the fine FE mesh.

The measure of strains used were the largest strains in the

structure. This consisted of the tensile and compressive

strains in the frames and helical ribs, and the tensile,

compressive and shears strains in the fuselage skin. These

strains are normalization with respect to the maximum

allowable strains in the structure. The margin of safety for

strain and strength response is defined as:

max

min

1 0, 1 0, 1 0S B

SMS MS MS

S

(2)

where MS is Margin of Safety, is the computed

strain, max is the maximum allowable strain, S is the

computed stiffness, Smin the minimum allowable stiffness, is

the computed linear buckling eigenvalue for the applied

loads.

V. DESIGN VARIABLES AND OPTIMIZATION OF FUSELAGE

STRUCTURE

The ALaSCA Airframe Concept is a lattice structure with a

load bearing skin and stiffeners located on either side of the

skin as shown in Fig. 3. The outer stiffeners are surrounded by

protective foam, which in turn is covered by a thin

aerodynamic skin [2]. The optimized grid type fuselage

section is a simple structure without windows or floors

consisting only of the repeated structural triangular unit cell.

Fig. 4 shows the finite element fuselage barrel model with the

inner helical ribs in green, their counter parts on the outside of

the skin in blue, the circumferential frames in yellow and the

skin in red. The stiffening ribs are arranged at an angle so as to

describe a helical path along the fuselage barrel skin. Hence,

these ribs are called helical ribs. The helical ribs have a hat

cross section, whereas the circumferential frames have a

Z-shaped cross section. These ribs in conjunction with the

circumferential frames create uniform triangular skin bays.

Fig. 3. Skin bay geometry.

Fig. 4. Circumferential ribs and helical ribs.

The design variables are chosen to vary the geometry of the

helical stiffeners and frames, the skin thickness, and the frame

pitch without altering the triangular shape of the skin bay

geometry. The seven optimization parameters are varied

between the maximum and the minimum bounds listed in

Table I. The design variables are shown in Fig. 3 and Fig. 4.

The optimization constraints are strain, global stiffness and

stability. The corresponding optimization responses extracted

from the FE models are the largest strains (tensile and

compressive strains in the frames and in the helical ribs;

tensile, compressive and shear strains in the skin), the critical

buckling load, and the stiffness of the fuselage. The composite

material fails if it is strained beyond a maximum value.

Finally, the fuselage has to have a certain stiffness in bending

and in torsion to avoid excessive global deformations in flight.

The design variables are varied within the bounds shown in

Table I to generate fuselage structures, which are then

evaluated with respect to the mentioned failure modes.

An upward gust load case at low altitude and cruise speed is

applied to the modelled fuselage barrel and depicted in Fig. 5.

At one end of the barrel, bending, shear, and torsion loads are

applied while the opposite end is fixed. These loads are

International Journal of Materials, Mechanics and Manufacturing, Vol. 4, No. 3, August 2016

176

SQ

+

/

Binary Nodes

Unary Node

Terminal Nodes

x 1 x 2

x 3

Fig. 2. Typical tree structure for ./2

321 xxx

The helical ribs form an angle of 2φ between them as

illustrated in Fig. 3. This angle remains constant throughout

the barrel model.

International Journal of Materials, Mechanics and Manufacturing, Vol. 4, No. 3, August 2016

177

applied via rigid multipoint constrains, which force a rigid

barrel end. While floors are not modelled, the masses from the

floors are applied at the floor insertion nodes. Finally, the

structural masses are applied to the skin shell elements via

mass densities.

VI. RESULTS AND DISCUSSIONS

The explicit expressions for the responses related to tensile

strain, compressive strain, shear strain and weight of the

fuselage barrel are built by GP. As an example, the expression

for the shear strain is:

1 3 3 5 3 2 3 5

2 2 2

1 3 5 7 1 2 4 6 3 4 2 5

2 2 3

2 4 6 5 7 1 2 3

=1.26902 -1.76206 +0.00132105 +2.93847 / +603.316 / +

0.000000000604561 -4143.98 / ( )+ 163.814 / ( )+

0.202164 / ( )- 660.152 / (

ssf Z Z Z Z Z Z Z Z

Z Z Z Z Z Z Z Z Z Z Z Z

Z Z Z Z Z Z Z Z 2 2 4

4 7 1 6 7

4 2

2 3 4 5

) 15.5318 /

( ) 0.975381

Z Z Z Z Z

Z Z Z Z

where Z1 to Z7 are the design variables detailed in Table I.

The parametric optimization of the fuselage barrel was

performed by a Genetic Algorithm (GA) used on the

GP-derived analytical metamodels. Since a GA has good

non-local properties and is capable of solving problems with a

mix of continuous and discrete design variables, it becomes a

good choice for the fuselage barrel optimization where one of

the design variables, the number of helical ribs, is integer. The

results of the metamodel-based optimization and the fine

mesh FE analysis are given in Table II.

TABLE I: DESIGN VARIABLES

Design variables Lower bound

[mm]

Upper bound

[mm]

Skin thickness (h) 0.6 4.0

Number of helical rib pairs, (n) 50 150

Helical rib thickness, (th) 0.6 3.0

Helical rib height, (Hh) 15 30

Frame pitch, (d) 500 650

Frame thickness, (tf) 1.0 4.0

Frame height, (Hf) 50 150

TABLE II: STRUCTURAL RESPONSE VALUES FOR THE OPTIMUM DESIGN

Response type Strain

tension

Strain

compression

Strain

shear Buckling

Torsional

stiffness

Bending

stiffness Normalized mass

Prediction by metamodel 0.20 0.23 1.27 0.00 1.21 0.89 0.29

Fine mesh FE analysis 0.62 0.08 1.09 -0.07 1.21 0.89 0.29

Composite laminate

(±45/90/45/0/-45/0)s 1.15 0.19 1.31 0.13 1.25 0.81 0.29

TABLE III: DESIGN VARIABLE VALUES FOR THE OPTIMAL DESIGN

Design variable Skin thickness

(h), mm

No. of helical

rib pairs, (n)

Helical rib

thickness, (th), mm

Helical rib height,

(Hh), mm

Frame pitch,

(d), mm

Frame thickness,

(tf), mm

Frame height,

(Hf), mm

Optimum value 1.71 150.00 0.61 27.80 501.70 1.00 50.00

Results in Table II show that buckling is the driving

criterion in obtaining the optimum. The metamodel-predicted

optimum has a critical margin of buckling of 0.00 with a

normalized weight of 0.29. However, when this was checked

with a finite element analysis using a fine mesh, this value was

found to be -0.07 that is unacceptable. This issue has to be

addressed by interpreting the skin as a valid

compositelaminate at the end of this Section.

Fig. 5. Load application.

The predicted tensile strain margin of 0.20 is conservative

when compared the 0.62 margin obtained by the FE analysis.

The predicted compressive and shear strain of 0.23 and 1.27,

respectively, are not conservative compared to the

compressive strain margin of 0.08 and the shear margin of

1.09 obtained by the FE analysis. This is acceptable as these

are not the critical margins. The predicted stiffness margins

are the same as the margins obtained by the FE analysis but do

not act as critical constraints in this design optimization

problem. The design variable set for the final optimum

geometry is listed in Table III. The length of the frame pitch is

501.7 mm which is close to the lower bound of 500. The

resulting small triangular skin bays have a base width of 83.78

mm, a height of 501.7 mm and a small angle between the

crossing helical ribs of 2φ=9.55°. Such small and

skinny-triangular skin bays are excellent against buckling.

There is a good correspondence of the obtained results with

the analytical estimates of DLR that produced the value of

2φ=12° [10].

Since the optimal design only used smeared ply properties,

the skin thicknesses had to be corrected to account for a

standard CFRP ply thickness of 0.125 mm. This means that

the skin thickness is increased from 1.71 mm to 1.75 mm and

plies of 0°, 45°, -45° and 90° orientation arranged in a

balanced and symmetric laminate have to be used to comply

with the aircraft industry lay-up rules and manufacturing

requirements [11]-[13]. The structural responses obtained by

the FE analysis with the (±45/90/45/0/-45/0)s laminate skin

are given in Table II.

Incorporating the ply thicknesses into the design has

increased the buckling margin of safety making all margins

positive. Therefore a light-weight design which fulfils the

stability, global stiffness and strain requirements has been

obtained.

VII. CONCLUSION

Parametric optimization was applied to the detailed design

of a fuselage barrel section by using Genetic Algorithms on a

metamodel generated with Genetic Programming. The

optimum structure was obtained by performing parametric

optimization subject to stability, global stiffness and strain

requirements, then its optimal solution and structural

responses were verified by finite element simulations. The

stability criterion is the driving factor for the skin bay size and

the fuselage weight. By interpreting the skin modelled with

smeared ply properties as a real-life composite laminate, a

practical lay-up with a standard ply thickness of 0.125 mm has

been obtained as (±45/90/45/0/-45/0)s. It is concluded that the

use of the global metamodel-based approach has allowed to

solve this optimization problem with sufficient accuracy as

well as provided the designers with a wealth of information on

the structural behaviour of the novel anisogrid composite

fuselage design.

REFERENCES

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2013.

Dianzi Liu was born in China and obtained his

PhD in mechanical engineering in the University

of Leeds, UK in 2010. His PhD research project

was bi-level optimization of composite aircraft

wing panels subject to manufacturing

constraints.

He has been a lecturer in engineering in the

University of East Anglia, Norwich, UK since

2014. Before joining the University, he spent three years in the University of

Leeds as a research fellow. His research interests focus on composite

structures, structural analysis, simulation and optimization driven designs,

implementation and application of optimization algorithms/techniques in

the mechanical, manufacturing and aerospace engineering.

Dr. Liu is a member of South Asia Institute of Science and Engineering

(SAISE), a member of American Institute of Aeronautics and Astronautics

(AIAA) and a member of International Society for Structural and

Multidisciplinary Optimization (ISSMO). Dr. Liu was awarded the

runner-up prize for his research paper in the ISSMO-Springer Prize

competition in 2009.

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